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1,\(a\left(b+c\right)+3b+3c=a\left(b+c\right)+3\left(b+c\right)=\left(b+c\right)\left(a+3\right)\)
2,\(a\left(c-d\right)+\left(c-d\right)=\left(c-d\right)\left(a+1\right)\)
3,\(mx+my+5x+5y=m\left(x+y\right)+5\left(x+y\right)=\left(x+y\right)\left(m+5\right)\)
4,\(4x+by+4y+bx=4\left(x+y\right)+b\left(x+y\right)=\left(x+y\right)\left(4+b\right)\)
5,\(1-ax-x+a=\left(1-x\right)+a\left(1-x\right)=\left(1-x\right)\left(a+1\right)\)
\(a,\left(2a+3\right)x-\left(2a+3\right)y+\left(2a+3\right)\)
\(=\left(2a+3\right)\left(x-y+1\right)\)
\(b,\left(4x-y\right)\left(a-1\right)-\left(y-4x\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)
\(=\left(4x-y\right)\left(a-1\right)+\left(4x-y\right)\left(b-1\right)+\left(4x-y\right)\left(1-c\right)\)
\(=\left(4x-y\right)\left(a-1+b-1+1-c\right)\)
\(=\left(4x-y\right)\left(a+b-c-1\right)\)
\(c,x^k+1-x^k-1\)
\(=0?!?!\)
\(d,x^m+3-x^m+1\)
\(=4\)
\(e,3\left(x-y\right)^3-2\left(x-y\right)^2\)
\(=\left(x-y\right)^2\left(3\left(x-y\right)-2\right)\)
\(=\left(x-y\right)^2\left(3x-3y-2\right)\)
\(f,81a^2+18a+1\)
\(=\left(9a\right)^2+2.9a+1\)
\(=\left(9a+1\right)^2\)
\(g,25a^2.b^2-16c^2\)
\(=\left(5ab\right)^2-\left(4c\right)^2\)
\(=\left(5ab+4c\right)\left(5ab-4c\right)\)
\(h,\left(a-b\right)^2-2\left(a-b\right)c+c^2\)
\(=\left(a-b-c\right)^2\)
\(i,\left(ax+by\right)^2-\left(ax-by\right)^2\)
\(=\left(ax+by-ax+by\right)\left(ax+by+ax-by\right)\)
\(=2by.2ax\)
\(=4axby\)
a) \(A=5\left(x-y\right)+ax-ay=\left(a+5\right)\left(x-y\right)\)
b) \(B=a\left(x+y\right)-4x-4y=\left(x+y\right)\left(a-4\right)\)
c) \(C=xz+yz-5\left(x+y\right)=\left(x+y\right)\left(z-5\right)\)
d) \(D=a\left(x-y\right)+bx-by=\left(a+b\right)\left(x-y\right)\)
e) \(E=x\left(x+y\right)-5x-5y=\left(x-5\right)\left(x+y\right)\)
f) \(F=x^2-x-y^2-y=\left(x-y\right)\left(x+y\right)-\left(x+y\right)=\left(x+y\right)\left(x-y-1\right)\)
g) \(G=x^2-xy+x-y=x\left(x-y\right)+x-y=\left(x+1\right)\left(x-y\right)\)
A = 5(x - y) + ax - ay = 5(x - y) + a(x - y) = (a + 5)(x - y)
B = a(x + y) - 4x - 4y = a(x + y) - 4(x + y) = (a - 4)(x + y)
C = xz + yz - 5(x + y) = z(x + y) - 5(x + y) = (z - 5)(x + y)
D = a(x - y) + bx - by = a(x - y) + b(x - y) = (a + b)(x - y)
E = x(x + y) - 5x - 5y = x(x + y) - 5(x + y) = (x - 5)(x + y)
F = x2 - x - y2 - y = (x2 - y2) - (x + y) = (x2 - xy + xy - y2) - (x + y) = [x(x - y) + y(x - y)] - (x + y) = (x - y)(x + y) - (x + y) = (x + y)(x - y - 1)
G = x2 - xy + x - y = x(x - y) + (x - y) = (x + 1)(x - y)
a) 3x^2(x+1)-2(x+1)
= (3x^2-2)(x+1)
b) a(b+c)+3b+3c
= a(b+c) +3(b+c)
= (a+3)(b+c)
c) b(a-c) + 5a-5c
= b(a-c) + 5(a-c)
= (b+5)(a-c)
d) a(m-n) + m-n
= a(m-n) + (m-n)
= (a+1)(m-n)
\(a.a\left(m-n\right)+m-n\)
\(=a\left(m-n\right)+\left(m-n\right)\)
\(=\left(a+1\right)\left(m-n\right)\)
\(b.ma+mb-a-b\)
\(=m\left(a+b\right)-\left(a+b\right)\)
\(=\left(m-1\right)\left(a+b\right)\)
\(c.4x+by+4y+bx\)
\(=\left(4x+4y\right)+\left(bx+by\right)\)
\(=4\left(x+y\right)+b\left(x+y\right)\)
\(=\left(b+4\right)\left(x+y\right)\)
\(d.1-ax-x+a\)
\(=\left(a-ax\right)+\left(1-x\right)\)
\(=a\left(1-x\right)+\left(1-x\right)\)
\(=\left(a+1\right)\left(1-x\right)\)
1.a(m-n)+m-n=am-an+m-n=(am+m)-(an+n)=m(a+1)-n(a+1)=(a+1)(m-n)
2.ma+mb-a-b=(ma-a)+(mb-b)=a(m-1)+b(m-1)=(m-1)(a+b)
3.4x+by+4y+bx=(4x+bx)+(4y+by)=x(4+b)+y(4+b)=(4+b)(x+y)
4.1-ax-x+a=(1+a)-(ax+x)=(1+a)-x(a+1)=(1+a)(1-x)
A = 4acx + 4bcx + 4ax + 4bx ( đã sửa '-' )
= 4x( ac + bc + a + b )
= 4x[ c( a + b ) + ( a + b ) ]
= 4x( a + b )( c + 1 )
B = ax - bx + cx - 3a + 3b - 3c
= x( a - b + c ) - 3( a - b + c )
= ( a - b + c )( x - 3 )
C = 2ax - bx + 3cx - 2a + b - 3c
= x( 2a - b + 3c ) - ( 2a - b + 3c )
= ( 2a - b + 3c )( x - 1 )
D = ax - bx - 2cx - 2a + 2b + 4c
= x( a - b - 2c ) - 2( a - b - 2c )
= ( a - b - 2c )( x - 2 )
E = 3ax2 + 3bx2 + ax + bx + 5a + 5b
= 3x2( a + b ) + x( a + b ) + 5( a + b )
= ( a + b )( 3x2 + x + 5 )
F = ax2 - bx2 - 2ax + 2bx - 3a + 3b
= x2( a - b ) - 2x( a - b ) - 3( a - b )
= ( a - b )( x2 - 2x - 3 )
= ( a - b )( x2 + x - 3x - 3 )
= ( a - b )[ x( x + 1 ) - 3( x + 1 ) ]
= ( a - b )( x + 1 )( x - 3 )
A = xy + y - 2x - 2
= y( x + 1 ) - 2( x + 1 )
= ( x + 1 )( y - 2 )
B = x2 - 3x + xy - 3y
= x( x - 3 ) + y( x - 3 )
= ( x - 3 )( x + y )
C = 3x2 - 3xy - 5x + 5y
= 3x( x - y ) - 5( x - y )
= ( x - y )( 3x - 5 )
D = xy + 1 + x + y
= y( x + 1 ) + ( x + 1 )
= ( x + 1 )( y + 1 )
E = ax - bx + ab - x2
= ( ax - x2 ) + ( ab - bx )
= x( a - x ) + b( a - x )
= ( a - x )( x + b )
F = x2 + ab + ax + bx
= ( ax + x2 ) + ( ab + bx )
= x( a + x ) + b( a + x )
= ( a + x )( x + b )
G = a3 - a2x - ay + xy
= a2( a - x ) - y( a - x )
= ( a - x )( a2 - y )
Bonus : = ( a - x )[ a2 - ( √y )2 ]
= ( a - x )( a - √y )( a + √y )
H = 2xy + 3z + 6y + xz
= ( 6y + 2xy ) + ( 3z + xz )
= 2y( 3 + x ) + z( 3 + x )
= ( 3 + x )( 2y + z )
A = xy + y - 2x - 2 = y(x + 1) - 2(x + 1) = (y - 2)(x + !1
B = x2 - 3x + xy - 3y = x(x - 3) + y(x - 3) = (x + y)(x - 3)
C = 3x2 - 3xy - 5x + 5y = 3x(x - y) - 5(x - y) = (3x - 5)(x - y)
D = xy + 1 + x + y = xy + x + y + 1 = x(y + 1) + (y + 1) = (x + 1)(y + 1)
E = ax - bx + ab - x2 = ax - x2 + ab - bx = a(a - x) - b(a - x) = (a - b)(a - x)
F = x2 + ab + ax + bx = ab + ax + bx + x2 = a(b + x) + x(b + x) = (a + x)(b + x)
G = a3 - a2x - ay + xy = a2(a - x) - y(a - x) = (a2 - y)(a - x)
H = 2xy + 3z + 6y + xz = 2xy + 6y + 3z + xz = 2y(x + 3) + z(x + 3) = (2y + z)(x + 3)
a) Ta có: \(a\left(m-n\right)+m-n\)
\(=a\left(m-n\right)+\left(m-n\right)\)
\(=\left(m-n\right)\left(a+1\right)\)
b) Ta có: \(mx+my+5x+5y\)
\(=m\left(x+y\right)+5\left(x+y\right)\)
\(=\left(x+y\right)\left(m+5\right)\)
c) Ta có: \(ma+mb-a-b\)
\(=m\left(a+b\right)-\left(a+b\right)\)
\(=\left(a+b\right)\left(m-1\right)\)
d) Ta có: \(1-xa-x+a\)
\(=\left(a+1\right)-x\left(a+1\right)\)
\(=\left(a+1\right)\left(1-x\right)\)
e) Ta có: \(\left(a-b\right)^2-\left(b-a\right)\left(a+b\right)\)
\(=\left(a-b\right)^2+\left(a-b\right)\left(a+b\right)\)
\(=\left(a-b\right)\left(a-b+a+b\right)\)
\(=2a\left(a-b\right)\)
f) Ta có: \(a\left(a-b\right)\left(a+b\right)-\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=\left(a+b\right)\left(a^2-ab\right)-\left(a+b\right)\left(a^2-ab+b^2\right)\)
\(=\left(a+b\right)\left(a^2-ab-a^2+ab-b^2\right)\)
\(=b^2\cdot\left(a+b\right)\)
g) Ta có: \(3x\left(x+7\right)^2-11x^2\left(x+7\right)+9\left(x+7\right)\)
\(=\left(x+7\right)\left[3x\left(x+7\right)-11x^2+9\right]\)
\(=\left(x+7\right)\left(3x^2+21x-11x^2+9\right)\)
\(=\left(x+7\right)\left(-8x^2+21x+9\right)\)
\(=\left(x+7\right)\left(-8x^2+24x-3x+9\right)\)
\(=\left(x+7\right)\left[-8x\left(x-3\right)-3\left(x-3\right)\right]\)
\(=\left(x+7\right)\left(x-3\right)\left(-8x-3\right)\)
h) Ta có: \(\left(x+5\right)^2-3\left(x+5\right)\)
\(=\left(x+5\right)\left(x+5-3\right)\)
\(=\left(x+5\right)\left(x+2\right)\)
i) Ta có: \(2x\left(x-3\right)-3\left(x-3\right)^2\)
\(=\left(x-3\right)\left[2x-3\left(x-3\right)\right]\)
\(=\left(x-3\right)\left(2x-3x+9\right)\)
\(=\left(x-3\right)\left(9-x\right)\)
j) Ta có: \(x\left(x-7\right)+\left(7-x\right)^2\)
\(=x\left(x-7\right)+\left(x-7\right)^2\)
\(=\left(x-7\right)\left(x+x-7\right)\)
\(=\left(x-7\right)\left(2x-7\right)\)
k) Ta có: \(3x\left(x-9\right)^2-\left(9-x\right)^3\)
\(=3x\left(x-9\right)^2+\left(x-9\right)^3\)
\(=\left(x-9\right)^2\cdot\left(3x+x-9\right)\)
\(=\left(x-9\right)^2\cdot\left(4x-9\right)\)
\(a.a\left(b+c\right)+3b+3c=a\left(b+c\right)+3\left(b+c\right)=\left(b+c\right)\left(a+3\right)\)
\(b.a\left(c-d\right)+c-d=\left(c-d\right)\left(a+1\right)\)
\(c.b\left(a-c\right)+5a-5c=b\left(a-c\right)+5\left(a-c\right)=\left(a-c\right)\left(b+5\right)\)
\(d.a\left(m-n\right)+m-n=\left(m-n\right)\left(a+1\right)\)
\(e.mx+my+5x+5y=m\left(x+y\right)+5\left(x+y\right)=\left(x+y\right)\left(m+5\right)\)
\(f.ma+mb-a-b=m\left(a+b\right)-\left(a+b\right)=\left(a+b\right)\left(m-1\right)\)
\(g.4x+by+4y+bx=4x+bx+by+4y=x\left(b+4\right)+y\left(b+4\right)=\left(b+4\right)\left(x+y\right)\)
\(h.1-ax-x+a=\left(a+1\right)-x\left(a+1\right)=\left(a+1\right)\left(1-x\right)\)
\(k.x^{m+2}-x^m=x^m\left(x^2-1\right)=x^m\left(x-1\right)\left(x+1\right)\)
\(m.\left(a-b\right)^2-\left(b-a\right)\left(a+b\right)=\left(b-a\right)^2-\left(b-a\right)\left(a+b\right)=\left(b-a\right)\left(b-a-a-b\right)=-2a\left(b-a\right)\)
\(n.a\left(a-b\right)\left(a+b\right)-\left(a^2-2ab+b^2\right)=a\left(a-b\right)\left(a+b\right)-\left(a-b\right)^2=\left(a-b\right)\left(a^2+ab-a+b\right)\)